Time-space trade-offs in population protocols for the majority problem.

Population protocols are a model for distributed computing that is focused on simplicity and robustness. A system of identical agents (finite state machines) performs a global task like electing a unique leader or determining the majority opinion when each agent has one of two opinions. Agents communicate in pairwise interactions with randomly assigned communication partners.

Weighted straight skeletons in the plane.

We investigate weighted straight skeletons from a geometric, graph-theoretical, and combinatorial point of view. We start with a thorough definition and shed light on some ambiguity issues in the procedural definition. We investigate the geometry, combinatorics, and topology of faces and the roof model, and we discuss in which cases a weighted straight skeleton is connected.

A simple algorithm for computing positively weighted straight skeletons of monotone polygons.

We study the characteristics of straight skeletons of monotone polygonal chains and use them to devise an algorithm for computing positively weighted straight skeletons of monotone polygons. Our algorithm runs in [Formula: see text] time and [Formula: see text] space, where denotes the number of vertices of the polygon.